#### Answer

$x=1$

#### Work Step by Step

In order to make the terms $2x$, $3x+2$, and $5x+3$ as consecutive terms in an arithmetic sequence, we must have a common difference between the terms.
For this, we have:
$(5x+3)-(3x+2) =(3x+2) -(2x)$
This yields:
$2x+1=x+2$
or, $2x-x=2-1$
or, $x=1$